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There were some other threads related to this, but I think the specific subject of the nominal current rating of various wire sizes, and the ability to handle overloads above those ratings, deserves separate attention. I just ran a test of #16 AWG magnet wire, which is conservatively rated at 7.5 to 10.5 amps, at 25 amps for a full minute without excessive heating, and also at about 85 amps for 10 seconds and 185 amps for over one second. It got hot, but survived with no burning or apparent damage.

 

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Since you're talking about magnet wire, what if you wind the wire into a multi-layer solenoid so that many of the turns don't see free air?

If you have a thermocouple datalogger handy, it would be interesting to see a temperature vs. time curve. Then you can figure out the heat dissipation time constant for that particular wiring configuration.
 
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